Battleship has always been my all time favorite game, in fact it was the very first one I bought when I got my new Motorola DROID. It's been that way ever since, and today it is available on the Android Market. Battleship can be downloaded for free from the Android Market, but the only problem you will have is trying to find an "official" Battleship ROM. It's easy enough to find some download zips, but most of them are not official.
There is an alternative for you though, it's called "Ce Jeu De Luxe", which translates as "Lucky Charm" in French. This download is actually much better quality than Battleship ROM and is actually considered by many to be the best version of the game. Ce Jeu De Luxe features high-quality artwork, a great interface, and an extremely challenging gameplay - all for free. One of the best things about it is that it supports Bluetooth and wireless gaming, so you can play Battleship on the go without having to worry about compatibility issues. In addition, it also has voice acting and lots of other neat features.
If you really want to play Battleship on your android phone, you can download this unceasingly updated game from the android market. As of this writing it has a full 25% discount, so you should definitely grab it while you can. The best thing about it is that it's perfect for almost any screen size, so you shouldn't have any trouble playing it on your phone. Furthermore, if you're someone who loves customization and would like to change things every now and again, then this game can certainly live up to your expectations. For a relatively cheap price, you get access to everything you need to make sure you enjoy every second of playing, including an awesome interface and a great game that's totally free to download.